Hitting times for the stochastic wave equation with fractional colored noise

被引：12
|
作者：
de la Cerda, Jorge Clarke [1 ,2 ,3 ]
Tudor, Ciprian A. [2 ,4 ]
机构：
[1] Univ Bio Bio, Fac Ciencias, Dept Matemat, Concepcion, Chile
[2] Univ Lille 1, Lab Paul Painleve, F-59655 Villeneuve Dascq, France
[3] Univ Concepcion, Dept Ingn Matemat, CI MA 2, Concepcion, Chile
[4] Acad Econ Studies, Bucharest, Romania
来源：
REVISTA MATEMATICA IBEROAMERICANA | 2014年 / 30卷 / 02期
关键词：
Stochastic wave equation; potential theory; hitting probability; capacity; Hausdorff dimension; spatially homogeneous Gaussian noise; fractional Brownian motion; Holder continuity; EVOLUTION-EQUATIONS; PROBABILITIES; DRIVEN; REGULARITY; DIMENSION; SYSTEMS;
D O I：
10.4171/RMI/796
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give sharp regularity results for the solution to the stochastic wave equation with linear fractional-colored noise. We apply these results in order to establish upper and lower bounds for the hitting probabilities of the solution in terms of the Hausdorff measure and the Newtonian capacity.
引用
收藏
页码：685 / 709
页数：25
相关论文
共 50 条
  • [41] Sharp space-time regularity of the solution to stochastic heat equation driven by fractional-colored noise
    Herrell, Randall
    Song, Renming
    Wu, Dongsheng
    Xiao, Yimin
    STOCHASTIC ANALYSIS AND APPLICATIONS, 2020, 38 (04) : 747 - 768
  • [42] Holder continuity of mild solutions of space-time fractional stochastic heat equation driven by colored noise
    Tran Thanh Binh
    Nguyen Huy Tuan
    Tran Bao Ngoc
    EUROPEAN PHYSICAL JOURNAL PLUS, 2021, 136 (09):
  • [43] Sample paths of the solution to the fractional-colored stochastic heat equation
    Tudor, Ciprian A.
    Xiao, Yimin
    STOCHASTICS AND DYNAMICS, 2017, 17 (01)
  • [44] Moderate Deviations for Stochastic Fractional Heat Equation Driven by Fractional Noise
    Sun, Xichao
    Li, Ming
    Zhao, Wei
    COMPLEXITY, 2018,
  • [45] Solving a Nonlinear Fractional Stochastic Partial Differential Equation with Fractional Noise
    Liu, Junfeng
    Yan, Litan
    JOURNAL OF THEORETICAL PROBABILITY, 2016, 29 (01) : 307 - 347
  • [46] Solving a Nonlinear Fractional Stochastic Partial Differential Equation with Fractional Noise
    Junfeng Liu
    Litan Yan
    Journal of Theoretical Probability, 2016, 29 : 307 - 347
  • [47] Bismut formula for a stochastic heat equation with fractional noise
    Yan, Litan
    Yin, Xiuwei
    STATISTICS & PROBABILITY LETTERS, 2018, 137 : 165 - 172
  • [48] The Influence of Noise on the Solutions of Fractional Stochastic Bogoyavlenskii Equation
    Al-Askar, Farah M.
    Mohammed, Wael W.
    Albalahi, Abeer M.
    El-Morshedy, Mahmoud
    FRACTAL AND FRACTIONAL, 2022, 6 (03)
  • [49] The density of the solution to the stochastic transport equation with fractional noise
    Olivera, Christian
    Tudor, Ciprian A.
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 431 (01) : 57 - 72
  • [50] STOCHASTIC CAHN-HILLIARD EQUATION WITH FRACTIONAL NOISE
    Bo, Lijun
    Jiang, Yiming
    Wang, Yongjin
    STOCHASTICS AND DYNAMICS, 2008, 8 (04) : 643 - 665
12345